What is the solution for (dy)/(dx)-2xy=15x^2e^{x^2} ?

The solution for (dy)/(dx)-2xy=15x^2e^{x^2} is y=5e^{x^2}x^3+c_{1}e^{x^2}

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(dy)/(dx)-2xy=15x^2e^{x^2}

\frac{d y}{d x} - 2 x y = 15 x^{2} e^{x^{2}}

y = 5 e^{x^{2}} x^{3} + c_{1} e^{x^{2}}

Solution steps

\frac{d y}{d x} - 2 x y = 15 x^{2} e^{x^{2}}

Solve linear ODE:

y = 5 e^{x^{2}} x^{3} + c_{1} e^{x^{2}}

y = 5 e^{x^{2}} x^{3} + c_{1} e^{x^{2}}

\frac{\partial}{\partial x} (x y (2 + x) (y - 3))

x^{2} \frac{d y}{d x} = y - x y, y (- 1) = - 5

\frac{d}{d x} (7 e^{x} - (\frac{10}{x ^{4}}))

f (x) = \frac{2 - \frac{1}{x}}{x - 3}

x \to - 2 - lim (g (x))

What is the solution for (dy)/(dx)-2xy=15x^2e^{x^2} ?
The solution for (dy)/(dx)-2xy=15x^2e^{x^2} is y=5e^{x^2}x^3+c_{1}e^{x^2}